Numeracy Practice. Dice

Numeracy practice tests

Firstly, this page focuses on free numeracy practise tests, tips and NHS nursing numeracy test practice.

Secondly, the first section below is for psychometric test practice tailored to specific careers.

Thirdly, here’s our literacy tips page, which includes our free practice literacy test.

Introduction to Numeracy tests

A typical numeracy test measures an individual’s ability to use addition, subtraction, multiplication, and division.

Here are some examples of the Navy numeracy test:

Example Numeracy Tests

Navy Practice Test (Number Series)

Practice Test Answers (Number Series)

Navy Practice Test 2 (Number Series)

Practice Test 2 answers (Number Series)

1) What is the number 55.368 to two decimal places?

A  55.30

B  55.35

C  55.36

D  55.37

E   55.40

2) Add 456 to 9322

– – –  Numeracy test practice – – –

A  9678

B  9687

C  9778

D  9787

E   9788

3) What is 40% of 5000?

A  2000

B  2500

C  3000

D  3500

E   4000

4) A garden measures 20m by 15m. What is the area of the garden, in square metres?

A  150 square metres

B  200 square metres

C  250 square metres

D  300 square metres

E   350 square metres

– – –  Numeracy test practice – – –

5) Subtract 99.1 from 144.9

A  45.9

B  45.8

C  45.7

D  45.6

E   45.5

Numeracy Tips

This is our numeracy practice test. And these are our numeracy practice test answers.

Numeracy practise. Answering questions

Our numeracy test practice

This is our Numerical Reasoning Practice Test for your free practice. And here are the respective numerical reasoning online practice test answers.

Also, our Mental Arithmetic Practice Test for your practice. And here are the respective Mental Arithmetic practice test answers.

What are numeracy skills?

The most basic type of numeracy tips relates to the four basic mathematical operators.                     

Numeracy Test Tips

  • Start by calculating the difference between the first and second, and the second and third numbers. Can you see a pattern? If so it is likely to be a pattern based upon addition or subtraction. Is the sequence-based upon adding
  • The same number each time ?
  • Two numbers together each time?
  • Is the sequence-based upon subtracting the same number each time?
  1. If the series does not appear to be based upon addition or subtraction then the next option to consider is that it is based upon multiplication – for example multiplying by the same number each time.
  2. If this doesn’t provide a solution then consider whether it looks like two different series of numbers – rather than the more commonly found single series.
  3. Now you need to start thinking outside of the box. Try not to think in terms of the traditional counting system 1, 2, 3.

What is a numeracy test?

There are many different psychometric tests like the aptitude test, personality test, verbal reasoning, inductive reasoning, logical reasoning, attention to detail, leadership test and many more. Well, numerical reasoning assessment is one of them. This is where all the graphs, long numbers and equations play an important role. Since this is based on mathematics, the main objective of numerical reasoning assessment is to check the ability of the candidates to work with numerical information.

The numerical reasoning assessment is often a written test having a given time limit and its structure can be unconventional. The candidates taking this test often find it to be tricky or challenging when they compare it with their school or college level numerical tests.

Numeracy Skills Practice

We hope you enjoy all of our free numeracy skills practice. Below is our Parents Guide to numeracy skills practice.

Parents Guide to Numeracy Skills Practice

– – – Numeracy Skills Practice – – –

How difficult are numeracy tests?

The difficulty level of the test you take will reflect the level of numerical reasoning knowledge needed in the position or place you are applying for. The numerical reasoning practice tests in Part II of this book span a wide range of difficulty levels. This is deliberate and reflects the range of tests in current usage. Starting with the easiest and getting increasingly difficult, the practice questions cover the full range of numerical reasoning ability.

We think that the best order of priorities for practising any sort of numerical reasoning test is to ensure you have the basic numeracy skills by taking these Mental Maths Tests.

Then to move on to some numerical reasoning practice. Finally, to practice with psychometric test publisher Websites.

Numeracy Test Intro

Numeracy reasoning tests are used to measure different forms of numerical reasoning ability, particularly the identification of trends in large sets of numerical data and the interpretation of tables/graphs. Thus numerical reasoning tests – especially those that are set at a higher level – ask candidates to analyse numerical information presented as line graphs, histograms, pie-charts, tables, etc.

In summary, numerical reasoning tests also ask candidates to: interpret statistics and other financial information; problem solve and apply your findings to a new numerical reasoning problem; use mathematical operations (e.g. fractions, ratios, percentages); and more specific operations, such as number distance, to solve numerical reasoning problems.

– – – Numeracy Skills Practice – – –

What do numeracy tests measure?

In simple terms a numerical reasoning test is a means of assessing a person’s ability to work with numbers.

At the numeracy level, only the basic mathematical operations need to be understood. That includes fractions and decimals. 

For the 11 plus a wider numeracy skills base is required. To reach the pass level, a clear understanding of more complex mathematical operations is required. That means having a thorough understanding of ratios and percentages.

As well as how to interpret figures within numerical reasoning questions. These are written as a one to two sentence question. The 11 Plus Maths requirements also include working competently with financial figures, weights and other measures.

Numeracy practice test tips

Usually, candidates are provided with a variety of questions in accordance with the rule of one question = one minute.

Certain numeracy tests have a repeated pattern and this gives you an idea on how to prepare for it. So, ensure that you practice these portions thoroughly and make yourself comfortable with the different types of questions in these areas.

There are always some tips that you can utilize while preparing for your numerical reasoning assessment which are as follows. These tips will easily help you to get through the numerical reasoning assessment easily.

Start by calculating the available time per question. This will ensure you do not spend too much time per question.

Numeracy practice skills

More Numeracy Tips

  • While you are practising for the test, try doing it in the same way in which you’ll be sitting your real numerical reasoning assessment. Take your seat in a quiet surrounding with as less distraction as possible at a table. This will increase your focus and also make silence less intimidating and let you practice more thoroughly.
  • The numerical reasoning assessment will definitely not kill you but try to figure out the areas that you are getting wrong most of the time and practice those areas thoroughly. Focusing on those problems will help you to improve your overall test.
  • Thus, following these tips can be really helpful during the day of your numerical reasoning assessment. Do not stress. So, the type of job position you are applying for doesn’t matter, as it can be an investment bank, consultancy firm or the position of a manager, it is compulsory for you to take the numerical reasoning test.

Aptitude Test Design Projects

Rob Williams has over twenty years experience of bespoke psychometric test design, especially aptitude test designs. Plus ten years prior to this spent working for several of the UK’s leading test publishers. These include IBM, OPP, SHL and HireVue.

Our consultancy work focuses on graduate assessment designs and aptitude test designs. 

Bespoke graduate assessment designs

In fact it is bespoke aptitude designs which are our speciality. Otherwise known as company-specific tests. With a bespoke psychometric test, organisations can design the content of their test(s) to match their own industry sector.

Understanding graduate assessments gives those applicants a competitive edge in today’s job market.

At a time when the graduate market is at its most competitive it pays for all graduates to perform their best on these psychometric tests. It makes sense to be prepared. Fortunately, there is a wide variety of practice material available, allowing graduates to familiarize themselves with the sort of tests they’ll encounter as part of the recruitment process.

Graduate assessment design

Graduate recruiters who want to minimise recruitment costs see online ability tests as an efficient and effective means of sifting the initial applicant pool. Verbal and numerical reasoning tests offer a reliable and standardised way to ensure that an optimal number of good candidates are seen by the business at the much more expensive ‘face-to-face’ stage. Chances are that this next stage will involve a retest in order to verify that the candidate who took the online test was who they said they were!

Online testing is particularly attractive for the ease with which multinational organisations can offer the same test(s) in a wide range of different languages to graduates around the world. The use of standardised tests in the recruitment process helps to ensure that applicants from different countries and from different ethnic groups are treated fairly.

We believe in the benefits of practice and ensuring fairness in testing. We, therefore, offer some practice aptitude tests and some practice psychometric tests. The intention is to promote as ‘level a playing-field’ as possible.

Bespoke aptitude test design

Our Personality test designs

Aptitude test solutions

Our consultancy work focuses on aptitude test practice and bespoke psychometric test design. We believe in the benefits of practice and ensuring fairness in testing. We, therefore, offer some practice aptitude tests and some practice psychometric tests. The intention is to promote as ‘level a playing-field’ as possible.

Aptitude test design – Employability

All of our psychometric test practice resources are free. So, we hope you enjoy using them!   In our opinion, there is plenty of the right type of aptitude test practice, aptitude test tips and test-taking strategies.

We certainly hope you get maximum value from our free psychometric test practice resources!  Psychometric test practise works best when it’s specific to the test type and the level of difficulty of the psychometric test you will be taking.

Graduate Assessment designs for aptitude

Our first point is that a well-designed selection procedure focuses on predicting a graduate’s competence within a particular work context.

Secondly, that psychometric assessments only form one part of the selection procedure.

Our third point is that personality assessments can give an indication of how well an individual applicant will fit into the existing workplace or team.

Finally, psychometric assessments can assess which applicants are most suited to the demands of the vacant job in terms of both ability and personality factors.

Aptitude test design example

Firstly, it’s fundamental to the use of any psychometric test is that users are aware of a test’s effectiveness and its known limitations.  This information is calculable through knowledge of a measure’s reliability and validity. 

Secondly, importance is attached to test results and decisions are made using test data.  Thirdly, you must be sure that the tests you are using have sound credentials and have been properly developed.

Three key psychometric pillars

These are often taken for granted – due to the fine efforts of HireVue’s and MindX’s R&D teams’ conscientious work!

  1. Standardization
  2. Reliability – means if I take the same test next week, my results will be similar.
  3. Validity – means the test measures what it says it measures. MindX knows which personality traits are measured because we have compared our results to well-established personality tests. HireVue validates its video assessments using high performer data and job analysis results.
  4. Being Non-discriminatory

 1. Standardization  

Since the first IQ tests were developed the whole point is to compare with a group of previous test-takers.

2. Reliability

There are two key types of psychometric reliability:

  • Test-Retest Reliability
  • Internal reliability.

Test-Retest Reliability

This concerns score consistency over time. If the test is measuring some stable characteristic of the individual such as intelligence, then the test should produce similar results if a group of candidates are examined using the same test at two points in time. The time gap between the measurement is important, as some psychological characteristics change considerably over time. Yet, a short gap of two weeks should not cause major changes.

Still, an external event in the period between the two assessment might cause a change, but here it is expected that the change will affect similarly all the candidates. This type of reliability is also known as test re-test reliability. It is assessed by correlating the tests scores measured first time with the test scores measured the second time. Ability tests are expected to have a reliability of at least r = .75, yet personality tests might have somewhat lower reliability.

Internal Consistency

The internal consistency refers to the question of whether all the test items measure the same concept. It can be assessed in two ways. The first method is known as the split-half reliability which require correlating the score based on half of the test items with the score based on the other half (e.g., scores on odd and even items). Alternative method is item-total reliability which requires correlating each item score with the total score of the rest of the items. There is a statistical measure called Cronbach alpha that summarises all the correlations into one figure. A test should have an alpha of at least a = .80.

Aptitude test’s psychometric terms


Every psychometric test has at least one norm group.

The standalone score has little meaning, so a comparison with previous candidate performance is used. For example, percentile rank.

Pre-test (or Pilot) Item

A trial item as part of a larger-than-necessary set of pre-test items. The  final, refined test is created by refining those items that work best. This is based on a statistical analysis of the trial item set’s results.

Aptitude Test Reliability

Firstly, is the test a reliable measure?

Most commonly the internal consistency index coefficient alpha or its dichotomous formulation, KR-20. Under most conditions, these range from 0.0 to 1.0, with 1.0 being perfectly reliable measurement. A reliable test may still not be a valid test.

Aptitude Test Validity 

Secondly, is the test valid? A measure of what it ‘says on the tin’?

In our opinion, both the initial content validation and later criterion validation analysis are vital for any bespoke psychometric test.

We recommend collecting additional recruitment data over time so that additional validation studies can be conducted. Such as assessment centre data.

There are many other types of psychometric test validation evidence, and one-off studies investigating a psychometric test’s criterion validity are common.

British Airways Aptitude Test Design Example

Blended assessment project:

  • Situational judgment test design;
  • Numerical reasoning test design;
  • Verbal reasoning test design
  • Personality questionnaire design.

For these two British Airways roles:

– Cabin crew assessment; and

– Customer service representative assessment.

British Army Aptitude Test Design Example

Psychometric lead role with Kenexa IBM; managing twenty associates.

  • We developed over twenty psychometric tests;
  • Situational judgement tests for Officers and for Soldiers;
  • Realistic job previews for Officers and for soldiers;
  • Ability tests (including problem-solving test) for Officers;
  • Ability tests (including a spatial reasoning test) for soldiers;
  • Officer personality questionnaire;
  • Soldier career guidance tools.

Aptitude Tests’ Vital Role

Many companies today are turning to testing and assessment tools to help them address these challenges and make more substantive and data-driven hiring decisions. Assessments are a great way to level the playing field and evaluate many candidates for the same skill sets in an objective fashion, using real-life technical scenarios that mirror the work they will be performing on the job. Automated assessment tools in particular can scale to make better use of your time and resources. Several key recruitment benefits are listed below.

Differentiation Benefits

Providing unbiased assessments is a great way to distinguish yourself to candidates in a crowded hiring environment. Candidates will see that you really care about hiring the most qualified tech workers in a manner that is unbiased and uncovers their true value.

Recruitment Cost and Recruitment Funnel Benefits

Automated testing helps you scale your recruiting efforts, evaluating many candidates simultaneously to save engineering hours, and ultimately the cost of those used hours, time and costs, which is particularly important for larger tech organizations.

Hiring, training and replacing a bad hire can cost almost 5x their annual salary. Making the right choice the first time around is vital to growing your business and keeping costs low.

Removing bias

Assessment tools give you a structured mechanism to remove bias from the evaluation and interview process. It’s completely objective, surfacing skill sets needed to succeed on the job without basing a decision on your intuition or gut feel. And it mitigates the disadvantage a candidate whose first language is not English may have in a traditional format.

Focusing on skills, not experience

Experience listed in a profile isn’t necessarily the most important indicator of true skills and expertise.

Assessments help you find candidates that may not have a lot of experience in a certain field. But nonetheless have the skills you’re looking for.

Consistent process benefits

Assessment tools help you standardize your ongoing evaluation process. You’ll get an objective look at how candidates perform in the testing phase and can then compare it to their success on the job. A post-mortem can reveal how a good (or bad) hire performed in the assessment and help you to duplicate (or avoid) that performance in the future.

Our Practice assessment books 

Passing Numerical Reasoning Tests book reviews

Buy this book to pass!

Brilliant book. Read it from cover to cover. Don’t skip the chapters. I know it can seem patronising, the way he breaks it down, but I’d recommend reading it through.

Brilliantly practical and informative

What a great practical book. It starts from what is a numerical reasoning test, covers why numerical reasoning tests are used, who/how we use numerical reasoning, tips for test day and even helps you brush up on your Maths skills – yes all those little shortcuts you wish you remembered. More than 3/4 of the book is dedicated to actual practice test and not only the answers are provided, but also an easy to follow explanation of each. Definitely a worthwhile buy.

Very clear layout to follow, questions advance over the …

Very clear layout to follow, questions advance over the chapters and it sets a steady pace. This book helped me immensely to get all the practice I needed within 3 days.

A really useful book 

Numerical Reasoning reviews

Another really useful book by Rob. I will be recommending this to my delegates on interviewing/assessment techniques training; clear, concise and, if you are applying for jobs with a strong numerical focus, the best £10 you will spend! I heartily recommend.

Five Stars

Great book and pretty hard numerical exercises.

Useful, informative and good value

A very user-friendly and easy to read guide. Really focuses your mind on brushing up on your Maths skills. The author explains clearly how you can prepare to give your best for a test. Very useful and highly recommended.

Five Stars

Great book, tons of info and test to help you understand.

Great to get some practical help on how to succeed … at this stage of selection. I will recommend to anyone who needs to get through a numerical reasoning test.

Passing Verbal Reasoning Tests book reviews

Brilliantly practical advice

The advice and practical examples will answer all your questions about an impending assessment. The book is easy to read and covers preparation, practical examples and an overview of the usual proceedings on test day.

The author also highlights questions to be asked before test day and (I was very pleased to see) encourages feedback after assessment. The recaps at the end of every chapter are great for a quick overview before test day. Definitely a worthwhile investment and sure to put you at ease before an assessment of this kind.

A MUST BUY for anyone attempting to pass any verbal reasoning test.

Verbal Reasoning reviews

An informative yet easy to read book which helped me get through graduate-level tests to the next stages of application. Would highly recommend.

Excellent sample tests and explanations

Passed the VRT for HMRC Legal Trainee Scheme this year after reading this book. Helpful.

Very useful and good practice

The book has a good range of tests that reflect what comes up in real tests – so pretty good practice for the real thing

Highly recommended

Just what I needed to further my career. Now I’ve tried the tests I feel more confident.

Good quality and light reading!

An excellent guide to performing well in verbal reasoning tests.

This book is an extremely well written and helpful guide for anyone needing guidance in how to perform well in verbal reasoning tests. There are plenty of examples of the different levels of tests. Clear explanations of the correct responses are given. I would definitely recommend this book to anyone who is facing taking verbal reasoning tests in pursuit of a new job or promotion.

numeracy test practice

Rob Williams Assessment – psychometric design specialists

Rob Williams Assessment Ltd has considerable experience in assessing test reliability test validity. This is one of the key final stages in any psychometric test design. Most recently we have been asked to validate situational judgement tests. In addition to testing the SJT reliability and to advise on suitable cut-off scores which minimise any adverse impact (due to gender, age, ethnic group and disability).

Many of the UK’s and US’s leading test publishers have used Rob Williams Assessment’s to assist with ensuring the psychometric properties of their trial psychometric tests. We consult on how to improve any test’s psychometric properties, particularly the test’s internal reliability and construct validity.

11+ Maths practice is our focus here.

11 Plus Maths Test-taking Strategies

Although there aren’t any quick wins for being good at Maths, some focussed test practice will improve your score – as will following a few test-taking strategies. As a timed test, you need to average around one minute per question. Work briskly but accurately. each question counts the same so pick off the easy ones first and don’t waste your test time on the most difficult questions.

Practise some of the most common numerical test types at the main test publisher websites. numerical reasoning test practise will prove to be an excellent means of brushing-up on any maths functions you haven’t used in a while. test pages these three sites cover most of the psychometric tests you are likely to find. For this reason alone I strongly advise practising sample questions from Kenexa-IBM TalentQ and SHL sites. ensure that you are comfortable using data tables, interpreting graphs and manipulating large financial figures.

numeracy test practice

Practice 11 Plus Maths questions

The table below shows the approximate flight distances of major airports from London.


If it takes approximately 10 hours to fly to Chicago from London, then how many hours would it take to fly to Sydney? (Assume that the same plane travels at the same average speed to each destination).

A                      B                      C                     D                     E

25                    26                    27                    28                    29

A flight from London to Rio de Janeiro is re-routed to Mexico City. In kilometres what is the difference in the flight distance now flown by the plane?

A                      B                      C                     D                     E

200 less           100 less           100 more         200 more         500 more

Two planes leave London half an hour apart. The first plane to leave arrives in Mexico City 15 hours later at 04.00. If both planes fly at the same speed, when does the second plane arrive in Rio de Janeiro?

A                      B                      C                     D                     E

04.00               04.15               04.20               04.25               04.30

numeracy test practice

Practice Maths questions

In a wrapping paper factory the size of paper is given in terms of X, Y and Z.  X=3Y, and 2Y = 9Z.

If a sheet of paper is 2X long, then how long is it in terms of Z?

A                      B                      C                     D                     E

27Z                  18Z                  9Z                    12Z                  6Z

If it costs £6.48 to produce a roll of paper 54Z long, how much does it cost to produce a roll of paper 6X long?

A                      B                      C                     D                     E

£12.96 £3.24               £9.72               £1.08               £4.32

If Y = 10cm, then what is the area of a piece of paper that is 2Y long and 2X wide?

A                      B                      C                     D                     E

12.00               0.12                 18.00               1.20                 1.80

Our 11 Plus Blog at sister site School Entrance Tests

Grammar School Entry / 11+ Maths practice / 11 Plus Maths Tips  / 11 Plus Non verbal reasoning tips / 11+ Exams Practice

Numeracy practice tests

Even more practice tests

For more Ten-minute practice tests, have a look at our Ten Minute Quizzes.

For more practice, register at Passed Papers to take a free verbal reasoning test. Practising this online test will help you to become familiar with taking online verbal reasoning tests.

Additional assessment practice

Numeracy practice tests